Problem: $K$ is the midpoint of $\overline{JL}$ $J$ $K$ $L$ If: $ JK = 8x + 9$ and $ KL = 5x + 27$ Find $JL$.
Solution: A midpoint divides a segment into two segments with equal lengths. ${JK} = {KL}$ Substitute in the expressions that were given for each length: $ {8x + 9} = {5x + 27}$ Solve for $x$ $ 3x = 18$ $ x = 6$ Substitute $6$ for $x$ in the expressions that were given for $JK$ and $KL$ $ JK = 8({6}) + 9$ $ KL = 5({6}) + 27$ $ JK = 48 + 9$ $ KL = 30 + 27$ $ JK = 57$ $ KL = 57$ To find the length $JL$ , add the lengths ${JK}$ and ${KL}$ $ JL = {JK} + {KL}$ $ JL = {57} + {57}$ $ JL = 114$